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Itô's Lemma: The Log Transform

Hard · Stochastic Calculus · Quant Trader interview question · Ito's Lemma, Stochastic Calculus, Geometric Brownian Motion, Log Transform

Suppose the price of a stock, $S_t$, follows a Geometric Brownian Motion (GBM) described by the following Stochastic Differential Equation (SDE): $dS_t = \mu S_t dt + \sigma S_t dW_t$, where $\mu$ is the constant drift, $\sigma$ is the constant volatility, and $W_t$ is a standard Brownian motion. Using Itô's Lemma, determine the stochastic differential equation for $Y_t = \ln(S_t)$.